You currently have $1, 000 in an account which pays a nominal rate of interest of...

You currently have $1, 000 in an account which pays a nominal rate of interest of 8% compounded quarterly. You plan to deposit $200 every two months with the first deposit one month from now. What will be the value of the account one month after the eighteenth deposit?
The answer is 5,331.95 but I dont know how to get it.

Expert Solution

Nominal rate = 8% Compunded Quarterly

Annual effective rate = (1+ 0.08/4)^4 -1 = 8.24%

Effective rate for 2 months = 8.24% /6 = 1.374% or 0.01374

Future value of the 2 month deposits one month after the eighteenth deposit=

A = 2 monthly deposit = $200

i = 2 monthly interest rate = 0.01374

n = total 2 months period = 18

=>Future value of the 2 month deposits =

=>Future value of the 2 month deposits= $4052.86

Monthly effective interest rate = 8.24% /12 =0.6867% or 0.006867

Future value of the present balance of $1000 after 36 months=$1000*(1+0.006867)^36

=>Future value of the present balance of $1000 after 36 months=$1279.35

henec total FV one month after the eighteenth deposit = $4052.86+$1279.35 = $5332.21

jeff jeffy answered 2 years ago

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